Question: 3 people can paint 6 walls in 46 minutes. How many minutes will it take for 7 people to paint 9 walls? Round to the nearest minute.
Answer: We know the following about the number of walls $w$ painted by $p$ people in $t$ minutes at a constant rate $r$ $w = r \cdot t \cdot p$ $\begin{align*}w &= 6\text{ walls}\\ p &= 3\text{ people}\\ t &= 46\text{ minutes}\end{align*}$ Substituting known values and solving for $r$ $r = \dfrac{w}{t \cdot p}= \dfrac{6}{46 \cdot 3} = \dfrac{1}{23}\text{ walls painted per minute per person}$ We can now calculate the amount of time to paint 9 walls with 7 people. $t = \dfrac{w}{r \cdot p} = \dfrac{9}{\dfrac{1}{23} \cdot 7} = \dfrac{9}{\dfrac{7}{23}} = \dfrac{207}{7}\text{ minutes}$ $= 29 \dfrac{4}{7}\text{ minutes}$ Round to the nearest minute: $t = 30\text{ minutes}$